In my opinion, the use of VAR models is related to your analysis horizon and the number of observations. Do you have a long or short (but suffisant related to the number of variables) data?
1/ Case of large size sample: normally, most of macroeconomic and financial variables are integrated I(1) or more. In this situation we can apply the VECM framework (long term analysis) if the variables are cointegrated (Engle-Granger). Otherwise, we can use then a VAR (short-terme analysis) on the differenced variables (or detrended with other methods). We can use in some other situations the switching-regime models, threshold models, etc.
2/ Small size sample: if all variables in level are stationary (are I(0) without trend), we can use univariate regression model (ARDL).
The adequation between the multivariate analysis (definition of your variables) and economic theory is determinant.
In all of the situations, we should add the multivariate GARCH (BEKK) component if the GARCH effet is identified.
Yes in this case you can use VAR. However, I suggest to check the stantionarity of your series using other unit root tests such as PP and KPSS. If you have the same results, you need to to estimate VAR then, you can also try the SVAR.